Lens system, projection device, detecting module and electronic device

ABSTRACT

An electronic device includes a lens system including four lens elements. the four lens elements are, in order from an outer side to an inner side, a first lens element, a second lens element, a third lens element and a fourth lens element. The second lens element has negative refractive power. The fourth lens element has positive refractive power. At least one surface of the four lens elements has at least one inflection point. A projection device and a detecting module of the electronic device including the lens system are also disclosed.

RELATED APPLICATIONS

This application is a continuation patent application of U.S.application Ser. No. 16/584,699, filed on Sep. 26, 2019, which is acontinuation patent application of U.S. application Ser. No. 16/154,546,filed on Oct. 8, 2018, which is a continuation patent application ofU.S. application Ser. No. 16/007,901, filed on Jun. 13, 2018, whichclaims priority to Taiwan Application 106143064, filed on Dec. 8, 2017,which is incorporated by reference herein in its entirety.

BACKGROUND Technical Field

The present disclosure relates to a lens system, a projection device, adetecting module and an electronic device, more particularly to a lenssystem, a projection device and a detecting module applicable to anelectronic device.

Description of Related Art

With the popularity of electronic devices having camera functionalities,the demand of miniaturized optical systems has been increasing. A cameracapable of detecting three-dimensional (3D) information is favorable foroffering depth of field information on top of a two-dimensional (2D)image, thereby providing highly accurate and realistic user experience.When coupled with suitable optical elements or technologies, the cameracan further improve the 3D detection speed and resolution, and thus thecamera is applicable to augmented reality, face recognition, irisrecognition, gesture recognition, 3D modeling and so on.

Currently, the development of human-machine interaction is mostlylimited in 2D space. However, there are still some visual differencesbetween 2D image and real objects seen by naked eye. In order to improvethe users' immersion or convenience of living, capturing and utilizing3D information have become an important trend in the development offuture technology. The operation of 3D information capture involvesprojecting light from a light source with specific characteristics ontoan object, reflected by the object at different depths, and received byanother lens system. The reflected light is analyzed to obtain adistance between the camera and each position of the object at differentdepths for determining 3D structure of the object, or performing tasksby analyzing the message from the motion of the object. The variousapplications of 3D image capture and 3D image interaction are numerous,including face recognition systems, motion sensing gaming devices,augmented reality devices, driver assistance systems, smart electronicdevices, multi-camera devices, wearable devices, digital cameras,identification systems, entertainment devices, sports devices and smarthome systems, etc.

SUMMARY

According to one aspect of the present disclosure, an electronic deviceincludes a lens system including four lens elements. The four lenselements are, in order from an outer side to an inner side: a first lenselement, a second lens element, a third lens element and a fourth lenselement. The second lens element has negative refractive power. Thefourth lens element has positive refractive power. At least one surfaceof the four lens elements has at least one inflection point. When afocal length of the lens system is f, a focal length of the first lenselement is f1, a focal length of the second lens element is f2, a focallength of the third lens element is f3, a focal length of the fourthlens element is f4, a focal length of the i-th lens element is fi, anAbbe number of the first lens element is Vd1, an Abbe number of thesecond lens element is Vd2, an Abbe number of the third lens element isVd3, an Abbe number of the fourth lens element is Vd4, an Abbe number ofthe i-th lens element is Vdi, and an axial distance between the thirdlens element and the fourth lens element is T34, the followingconditions are satisfied:3.50<Σ|f/fi|, wherein i=1,2,3,4;40.0<ΣVdi<150.0, wherein i=1,2,3,4; andf/T34<10.0.

According to another aspect of the present disclosure, an electronicdevice includes a projection device including a lens system and at leastone light source. The lens system is operated within a wavelength rangeof 750 nm to 1500 nm. The at least one light source is disposed on aconjugate surface at an inner side of the lens system. The lens systemincludes four to six lens elements. At least one lens element of thelens system has an Abbe number smaller than 26.0. The lens systemincludes a first lens element closest to an outer side of the lenssystem and an inner lens element closest to the inner side of the lenssystem. When an axial distance between an outer-side surface of thefirst lens element and an inner-side surface of the inner lens elementis TD, the following condition is satisfied:1.0 [mm]<TD<5.0 [mm]

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be better understood by reading the followingdetailed description of the embodiments, with reference made to theaccompanying drawings as follows:

FIG. 1 is a schematic view of a projection device according to the 1stembodiment of the present disclosure;

FIG. 2 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 1stembodiment;

FIG. 3 is a schematic view of a projection device according to the 2ndembodiment of the present disclosure;

FIG. 4 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 2ndembodiment;

FIG. 5 is a schematic view of a projection device according to the 3rdembodiment of the present disclosure;

FIG. 6 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 3rdembodiment;

FIG. 7 is a schematic view of a projection device according to the 4thembodiment of the present disclosure;

FIG. 8 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 4thembodiment;

FIG. 9 is a schematic view of a projection device according to the 5thembodiment of the present disclosure;

FIG. 10 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 5thembodiment;

FIG. 11 is a schematic view of a projection device according to the 6thembodiment of the present disclosure;

FIG. 12 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 6thembodiment;

FIG. 13 is a schematic view of a projection device according to the 7thembodiment of the present disclosure;

FIG. 14 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 7thembodiment;

FIG. 15 is a schematic view of a projection device according to the 8thembodiment of the present disclosure;

FIG. 16 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 8thembodiment;

FIG. 17 is a schematic view of a projection device according to the 9thembodiment of the present disclosure;

FIG. 18 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 9thembodiment;

FIG. 19 is a schematic view of a projection device according to the 10thembodiment of the present disclosure;

FIG. 20 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 10thembodiment;

FIG. 21 is a schematic view of a projection device according to the 11thembodiment of the present disclosure;

FIG. 22 shows spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 11thembodiment;

FIG. 23 is a schematic view of a detecting module according to the 12thembodiment of the present disclosure;

FIG. 24 is a schematic view of an electronic device according to the13th embodiment of the present disclosure;

FIG. 25 is a schematic view of the detection of a 3D facial profile byusing the electronic device in FIG. 24;

FIG. 26 and FIG. 27 are schematic views of an electronic deviceaccording to another embodiment of the present disclosure;

FIG. 28 is a schematic view of an image recognition device according tothe 14th embodiment of the present disclosure;

FIG. 29 is a schematic view of inflection points and critical points onthe surfaces of lens elements, according to the 1st embodiment of thepresent disclosure; and

FIG. 30 is a schematic view of fitting structure disposed between everyadjacent lens element according to the 10th embodiment of the presentdisclosure.

DETAILED DESCRIPTION

A lens system includes four lens elements. The four lens elements are,in order from an outer side to an inner side, a first lens element, asecond lens element, a third lens element and a fourth lens element. Ifneeded, the lens system can include five or six lens elements; that is,the lens system further includes a fifth lens element and a sixth lenselement.

The first lens element can have positive refractive power; therefore, itis favorable for balancing the second lens element with negativerefractive power so as to reduce sensitivity of the lens system. Thefirst lens element can have an outer-side surface being convex in aparaxial region thereof; therefore, it is favorable for enhancing therefractive power of the first lens element so as to obtain a properprojection angle.

The second lens element can have negative refractive power. Therefore,it is favorable for correcting aberrations so as to improve opticalproperties, such as projection and imaging quality of the lens system.

The third lens element can have an outer-side surface being convex in aparaxial region thereof; therefore, it is favorable for correctingastigmatism so as to further improve image quality. The third lenselement can have an inner-side surface being concave in a paraxialregion thereof; therefore, it is favorable for suppressing the lightrefraction so as to reduce the chief ray angle.

The fourth lens element can have positive refractive power. Therefore,it is favorable for producing telecentric effect of light traveling tothe conjugate surface at the inner side of the lens system so as toenhance illuminance.

According to the present disclosure, among all surfaces of the four lenselements, there can be at least one surface having at least oneinflection point, and there can be at least one surface having at leastone critical point. Therefore, a lens surface having inflection point orcritical point is favorable for improving optical properties of the lenssystem as well as decreasing the required number of the lens elements soas to reduce the total track length; thus, the lens system is applicableto various electronic devices by satisfying the requirement ofcompactness. Please refer to FIG. 29, which is a schematic view ofinflection points F and critical points C on the surfaces of lenselements, according to the 1st embodiment of the present disclosure.

When a focal length of the lens system is f, a focal length of the firstlens element is f1, a focal length of the second lens element is f2, afocal length of the third lens element is f3, a focal length of thefourth lens element is f4, and a focal length of the i-th lens elementis fi, the following condition can be satisfied: 3.50<Σ|f/fi|, whereini=1, 2, 3, 4. Therefore, it is favorable for controlling a sum of therefractive power of every lens element of the lens system so as tobalance the distribution of refractive power and reduce the influence oftemperature variation on the lens system. Preferably, the followingcondition can also be satisfied: 4.50<Σ|f/fi|<25.0. More preferably, thefollowing condition can also be satisfied: 6.0<Σ|f/fi|<20.0.

When an Abbe number of the first lens element is Vd1, an Abbe number ofthe second lens element is Vd2, an Abbe number of the third lens elementis Vd3, an Abbe number of the fourth lens element is Vd4, and an Abbenumber of the i-th lens element is Vdi, the following condition can besatisfied: 40.0<ΣVdi<150.0, wherein i=1, 2, 3, 4. Therefore, it isfavorable for selecting the material of each lens element so as toenhance illuminance and further improve optical properties of the lenssystem. Preferably, the following condition can also be satisfied:40.0<ΣVdi<135.0. More preferably, the following condition can also besatisfied: 40.0<ΣVdi<120.0. According to the present disclosure, an Abbenumber Vd of a single lens element can be calculated by the followingformula: Vd=(Nd−1)/(NF−NC), wherein Nd is a refractive index of thesingle lens element for helium d-line (587.6 nm), NF is a refractiveindex of the single lens element for hydrogen F-line (486.1 nm), and NCis a refractive index of the single lens element for hydrogen C-line(656.3 nm).

When the focal length of the lens system is f, and an axial distancebetween the third lens element and the fourth lens element is T34, thefollowing condition can be satisfied: f/T34<10.0. Therefore, it isfavorable for producing a telecentric effect at the conjugate surface ofthe lens system for better image quality while improving lens assemblingyield rate.

When an axial distance between the outer-side surface of the first lenselement and an inner-side surface of the inner lens element is TD, thefollowing condition can be satisfied: 1.0 [mm]<TD<5.0 [mm]. Therefore,it is favorable for controlling the total track length of the lenssystem so as to maintain a compact size. When the lens system includesfour lens elements, TD is an axial distance between the outer-sidesurface of the first lens element and an inner-side surface of thefourth lens element. Preferably, the following condition can also besatisfied: 1.0 [mm]<TD<3.80 [mm].

According to the present disclosure, among all lens elements of the lenssystem, there can be at least one lens element having an Abbe numbersmaller than 26.0. Therefore, it is favorable for selecting the materialof lens element so as to enhance illuminance. Preferably, there can beat least one lens element having the Abbe number smaller than 22.0;alternatively, there can be at least two lens elements with each of themhaving an Abbe number smaller than 26.0. More preferably, there can beat least three lens elements with each of them having an Abbe numbersmaller than 26.0.

According to the present disclosure, the lens system can be operatedwith light having a wavelength range of 750 nanometers (nm) to 1500 nm.Therefore, a proper wavelength range of the lens system for imaging isfavorable for avoiding disturbance from the background noise so as toobtain proper detecting efficiency of the image sensor.

When a curvature radius of the outer-side surface of the third lenselement is R5, and a maximum effective radius of the outer-side surfaceof the third lens element is Y31, the following condition can besatisfied: |R5/Y31|<2.0. Therefore, it is favorable for controlling ashape of the outer-side surface of the third lens element so as toobtain a balance between compactness and good image quality. Preferably,the following condition can also be satisfied: |R5/Y31|<1.50.

When a central thickness of the first lens element 110 is CT1, a centralthickness of the second lens element is CT2, a central thickness of thethird lens element is CT3, a central thickness of the fourth lenselement is CT4, and a central thickness of the i-th lens element is CTi,the following condition can be satisfied: 1.0 [mm]<ΣCTi<2.50 [mm],wherein i=1, 2, 3, 4. Therefore, it is favorable for reducing the totaltrack length so as to keep the lens system compact.

When a maximum effective radius of the inner-side surface of the fourthlens element is Y42, and an entrance pupil diameter of the lens systemis EPD, the following condition can be satisfied: 0.10<(Y42×2)/EPD<1.20.Therefore, it is favorable for reducing the incident angle of light onthe conjugate surface at the inner side so as to enhance illuminance andimprove optical properties.

When a maximum value among all refractive indices of the lens system isNmax, the following condition can be satisfied: 1.50<Nmax<1.70.Therefore, it is favorable for selecting the material of lens element soas to reduce manufacturing costs and achieve compactness.

When an axial distance between the inner-side surface of the fourth lenselement and the conjugate surface is BL, and the focal length of thelens system is f, the following condition can be satisfied:0.01<BL/f<0.50. Therefore, it is favorable for providing a compactconfiguration featuring sufficient illuminance. Preferably, thefollowing condition can also be satisfied: 0.01<BL/f<0.15.

When a maximum effective radius of the outer-side surface of the firstlens element is Y11, and the maximum effective radius of the inner-sidesurface of the fourth lens element is Y42, the following condition canbe satisfied: 0.10<Y42/Y11<2.0. Therefore, it is favorable for improvinglens assembling yield rate, enlarging the field of light and maintainingthe intensity of light beams. Preferably, the following condition canalso be satisfied: 0.30<Y42/Y11<1.0.

When a maximum value among all maximum effective radii of all surfacesof the lens system is Ymax, the following condition can be satisfied:0.1 [mm]<Ymax<1.80 [mm]. Therefore, it is favorable for maintaining thecompact size of the lens system.

When a vertical distance between an inflection point closest to anoptical axis on any surface of the second lens element and the opticalaxis is Yp2x, a vertical distance between the inflection point closestto the optical axis on an outer-side surface of the second lens elementand the optical axis is Yp21, a vertical distance between the inflectionpoint closest to the optical axis on an inner-side surface of the secondlens element and the optical axis is Yp22, and the focal length of thelens system is f, the following condition can be satisfied:0.01<Yp2x/f<1.0, wherein x=1 or 2. Therefore, it is favorable forcorrecting aberrations so as to further improve optical properties.Preferably, the following condition can also be satisfied:0.01<Yp2x/f<0.50. FIG. 29 shows the inflection points F on the surfacesof the second lens element according to the 1st embodiment of thepresent disclosure.

According to the present disclosure, at least half of all lens elementsof the lens system can be made of plastic material, and all surfaces(outer-side surfaces and inner-side surfaces) of the plastic lenselements can be aspheric. Therefore, the material of lens element isproper for reducing costs and achieving compactness.

When a temperature coefficient of refractive index of eachaforementioned plastic lens element is dn/dt, the following conditioncan be satisfied: −150×10⁻⁶<dn/dt<−50×10⁻⁶ [1/° C.]. Therefore, it isfavorable for adjusting the material of lens element so as to keep thelens system compact and reduce manufacturing costs at various ambienttemperatures.

According to the present disclosure, a sum of central thicknesses of alllens elements of the lens system can range from 0.50 mm to 3.0 mm.Therefore, it is favorable for reducing the total track length so as tomaintain compactness.

According to the present disclosure, there can be at least one fittingstructure disposed between every adjacent lens element of the lenssystem. Therefore, it is favorable for providing proper concentricitybetween every adjacent lens element so as to correct aberrations due toa decentered lens element, thereby further improving image quality.Please refer to FIG. 30, which is a schematic view of fitting structuredisposed between every adjacent lens element according to the 10thembodiment of the present disclosure. For example, when an fittingstructure is disposed between the second lens element and the third lenselement, the second lens element typically includes a first axialassembling surface S1, and the third lens element includes a secondaxial assembling surface S2 corresponding to the first axial assemblingsurface S1. The first axial assembling surface S1 and the second axialassembling surface S2 can be assembled together to align the centers ofthe second lens element and the third lens element with each other,thereby obtaining high concentricity to reduce aberrations generated bythe decentered lens element.

According to the present disclosure, the lens system can be installed ina projection device, and the projection device can include at least onelight source. The light source can be a vertical-cavity surface-emittinglaser (VCSEL) so that it is favorable for providing a lens system with alight source featuring high directionality, low divergence and highintensity, thereby enhancing the illuminance of a projection surface.

According to the present disclosure, the projection device can includeat least one diffractive optical element, and the diffractive opticalelement can be disposed on the outer side of the first lens element.Therefore, it is favorable for diffracting light to increase the angleof projection, thereby enlarging the projection area.

According to the present disclosure, the projection device can beinstalled in an electronic device, and the electronic device can be aportable communication device such as a smartphone. Therefore, 3Ddetection, such as gesture recognition, face recognition and augmentedreality, can be introduced in the portable communication device for newuser experience, thereby accomplishing realistic and naturalhuman-machine interaction.

According to the present disclosure, the aforementioned features andconditions can be utilized in numerous combinations so as to achievecorresponding effects.

According to the present disclosure, the lens elements of the lenssystem can be made of either glass or plastic material. When the lenselements are made of glass material, the refractive power distributionof the lens system may be more flexible. The glass lens element caneither be made by grinding or molding. When the lens elements are madeof plastic material, the manufacturing cost can be effectively reduced.Furthermore, surfaces of each lens element can be arranged to beaspheric, which allows for more controllable variables for eliminatingthe aberration thereof, the required number of the lens elements can bedecreased, and the total track length of the lens system can beeffectively reduced. The aspheric surfaces may be formed by plasticinjection molding or glass molding.

According to the present disclosure, when a lens surface is aspheric, itmeans that the lens surface has an aspheric shape throughout itsoptically effective area, or a portion(s) thereof.

According to the present disclosure, each of an outer-side surface andan inner-side surface has a paraxial region and an off-axis region. Theparaxial region refers to the region of the surface where light raystravel close to the optical axis, and the off-axis region refers to theregion of the surface away from the paraxial region. Particularly,unless otherwise stated, when the lens element has a convex surface, itindicates that the surface is convex in the paraxial region thereof;when the lens element has a concave surface, it indicates that thesurface is concave in the paraxial region thereof. Moreover, when aregion of refractive power or focus of a lens element is not defined, itindicates that the region of refractive power or focus of the lenselement is in the paraxial region thereof.

According to the present disclosure, every parameter of the lens system,the projection device, the detecting module and the electronic device,unless specifically defined, is determined according to an operatingwavelength. For example, when the operating wavelength is visible light(e.g., a wavelength mainly in the range of 350˜750 nm), every parameteris determined and calculated according to d-line. When the operatingwavelength is near infrared light (e.g., a wavelength mainly in therange of 750˜1500 nm), every parameter is determined and calculatedaccording to the wavelength of 940 nm.

According to the present disclosure, an inflection point is a point onthe surface of the lens element at which the surface changes fromconcave to convex, or vice versa. A critical point is a non-axial pointof the lens surface where its tangent is perpendicular to the opticalaxis.

According to the present disclosure, the lens system can include atleast one stop, such as an aperture stop, a glare stop or a field stop.Said glare stop or said field stop is set for eliminating the straylight and thereby improving the image quality thereof.

According to the present disclosure, an aperture stop can be configuredas a front stop or a middle stop. A front stop disposed between adetected object and the first lens element can provide a longer distancebetween an exit pupil of the lens system and the conjugate surface toproduce a telecentric effect, and thereby reducing the chief ray angle.A middle stop disposed between the first lens element and the conjugatesurface is favorable for enlarging the viewing angle of the lens systemand thereby provides a wider field of view for the same.

According to the present disclosure, an outer side indicates the outsideof a mechanism, and an inner side indicates the inside of the mechanism.FIG. 23 is a schematic view of an imaging lens assembly 11 a of areceiving device 11 and a lens system 12 a of a projection device 12,according to an exemplary embodiment of the present disclosure. The lenssystem 12 a includes a conjugate surface 150 on the inner side, whichmeans that the conjugate surface 150 is a focal plane located on theinside of the mechanism (the conjugate surface on a reducing side). Theimaging lens assembly 11 a includes an image surface on the inner side,which means that the image surface is a focal plane located on theinside of the mechanism. As for the imaging lens assembly 11 a, theouter side of the imaging lens assembly 11 a is an object side of theimaging lens assembly 11 a, and the inner side of the imaging lensassembly 11 a is an image side of the imaging lens assembly 11 a. As forthe lens system 12 a of the projection device 12, the outer side of thelens system 12 a is a magnifying side of the lens system 12 a close to adetected object O, and a light emitting surface is on the outer side;the inner side of the lens system 12 a is a reducing side of the lenssystem 12 a close to a light source 160, and a light receiving surfaceis on the inner side. As for lens elements of the lens system 12 a, theouter side of any lens element thereof is a side of the lens elementclose to the detected object O, and an outer-side surface of the lenselement is a lens surface facing toward the detected object O; the innerside of the lens element is another side of the lens element close tothe light source 160 (or the conjugate surface 150), and an inner-sidesurface of the lens element is a lens surface facing toward the lightsource 160.

According to the above description of the present disclosure, thefollowing specific embodiments are provided for further explanation.

1st Embodiment

FIG. 1 is a schematic view of a projection device according to the 1stembodiment of the present disclosure. FIG. 2 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 1stembodiment. In FIG. 1, the projection device includes a lens system (itsreference numeral is omitted) of the present disclosure, a light source160, a diffractive optical element (DOE) 170 and a cover glass 180. Thelens system includes, in order from an outer side to an inner side, anaperture stop 100, a first lens element 110, a second lens element 120,a third lens element 130, a fourth lens element 140 and a conjugatesurface 150. The lens system includes four lens elements (110, 120, 130and 140) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 110 with positive refractive power has anouter-side surface 111 being convex in a paraxial region thereof and aninner-side surface 112 being convex in a paraxial region thereof. Thefirst lens element 110 is made of plastic material and has theouter-side surface 111 and the inner-side surface 112 being bothaspheric. Each of the outer-side surface 111 and the inner-side surface112 of the first lens element 110 has at least one inflection point.

The second lens element 120 with negative refractive power has anouter-side surface 121 being concave in a paraxial region thereof and aninner-side surface 122 being convex in a paraxial region thereof. Thesecond lens element 120 is made of plastic material and has theouter-side surface 121 and the inner-side surface 122 being bothaspheric. Each of the outer-side surface 121 and the inner-side surface122 of the second lens element 120 has at least one inflection point.Each of the outer-side surface 121 and the inner-side surface 122 of thesecond lens element 120 has at least one critical point.

The third lens element 130 with positive refractive power has anouter-side surface 131 being convex in a paraxial region thereof and aninner-side surface 132 being concave in a paraxial region thereof. Thethird lens element 130 is made of plastic material and has theouter-side surface 131 and the inner-side surface 132 being bothaspheric. Each of the outer-side surface 131 and the inner-side surface132 of the third lens element 130 has at least one inflection point. Theouter-side surface 131 of the third lens element 130 has at least onecritical point.

The fourth lens element 140 with positive refractive power has anouter-side surface 141 being convex in a paraxial region thereof and aninner-side surface 142 being convex in a paraxial region thereof. Thefourth lens element 140 is made of plastic material and has theouter-side surface 141 and the inner-side surface 142 being bothaspheric. The inner-side surface 142 of the fourth lens element 140 hasat least one inflection point and at least one critical point.

The light source 160 is disposed on or near the conjugate surface 150 ofthe lens system. The diffractive optical element 170 is made of silica.The diffractive optical element 170 and the cover glass 180 are locatedbetween the aperture stop 100 and the outer-side surface 111 of thefirst lens element 110, and will not affect the focal length of the lenssystem.

The equation of the aspheric surface profiles of the aforementioned lenselements of the 1st embodiment is expressed as follows:X(Y)=(Y ² /R)/(1+sqrt(1−(1+k)×(Y/R)²))+Σ_(i)(Ai)×(Y′),

where,

X is the relative distance between a point on the aspheric surfacespaced at a distance Y from an optical axis and the tangential plane atthe aspheric surface vertex on the optical axis;

Y is the vertical distance from the point on the aspheric surface to theoptical axis;

R is the curvature radius;

-   -   k is the conic coefficient; and

Ai is the i-th aspheric coefficient, and in the embodiments, i may be,but is not limited to, 4, 6, 8, 10 and 12.

In the lens system of the projection device according to the 1stembodiment, when a focal length of the lens system is f, an f-number ofthe lens system is Fno, and half of a maximum field of view of the lenssystem is HFOV, these parameters have the following values: f=3.18millimeters (mm), Fno=2.21, HFOV=13.0 degrees (deg.).

In this embodiment, the lens system is operated within an opticalspectrum having a center wavelength of λ nm, and the following conditionis satisfied: λ=940 nm.

When a maximum value among all refractive indices of the lens system isNmax, the following condition is satisfied: Nmax=1.634. In thisembodiment, the refractive index of the second lens element 120 islarger than the refractive indices of the first lens element 110, thethird lens element 130 and the fourth lens element 140, and thus Nmax isequal to the refractive index of the second lens element 120.

When an Abbe number of the first lens element 110 is Vd1, an Abbe numberof the second lens element 120 is Vd2, an Abbe number of the third lenselement 130 is Vd3, an Abbe number of the fourth lens element 140 isVd4, and an Abbe number of the i-th lens element is Vdi, the followingcondition is satisfied: ΣVdi=91.4, wherein i=1, 2, 3, 4.

When a central thickness of the first lens element 110 is CT1, a centralthickness of the second lens element 120 is CT2, a central thickness ofthe third lens element 130 is CT3, a central thickness of the fourthlens element 140 is CT4, and a central thickness of the i-th lenselement is CTi, the following condition is satisfied: ΣCTi=1.83 mm,wherein i=1, 2, 3, 4.

When an axial distance between an outer-side surface of an outer lenselement closest to the outer side of the lens system and an inner-sidesurface of an inner lens element closest to the inner side of the lenssystem is TD, the following condition is satisfied: TD=3.33 mm. In thisembodiment, the first lens element 110, which is the closest lenselement to the outer side, is interpret as the outer lens element, andthe fourth lens element 140, which is the closest lens element to theinner side, is interpret as the inner lens element. Thus, TD is equal toan axial distance between the outer-side surface 111 of the first lenselement 110 and the inner-side surface 142 of the fourth lens element140.

When a maximum value among all maximum effective radii of all surfacesof the lens system is Ymax, the following condition is satisfied:Ymax=0.88 mm. In this embodiment, a maximum effective radius of theinner-side surface 112 of the first lens element 110 is larger thanmaximum effective radii of the other surfaces (111, 121, 122, 131, 132,141 and 142), and thus Ymax is equal to the maximum effective radius ofthe inner-side surface 112 of the first lens element 110.

When the focal length of the lens system is f, a focal length of thefirst lens element 110 is f1, a focal length of the second lens element120 is f2, a focal length of the third lens element 130 is f3, a focallength of the fourth lens element 140 is f4, and a focal length of thei-th lens element is fi, the following condition is satisfied:Σ|f/fi|=8.35, wherein i=1, 2, 3, 4.

When the focal length of the lens system is f, and an axial distancebetween the third lens element 130 and the fourth lens element 140 isT34, the following condition is satisfied: f/T34=2.70. In thisembodiment, an axial distance between two adjacent lens elements is anair gap in a paraxial region between the two adjacent lens elements.

When an axial distance between the inner-side surface 142 of the fourthlens element 140 and the conjugate surface 150 is BL, and the focallength of the lens system is f, the following condition is satisfied:BL/f=0.04.

When a curvature radius of the outer-side surface 131 of the third lenselement 130 is R5, and the maximum effective radius of the outer-sidesurface 131 of the third lens element 130 is Y31, the followingcondition is satisfied: |R5/Y31|=0.76.

When the maximum effective radius of the outer-side surface 111 of thefirst lens element 110 is Y11, and the maximum effective radius of theinner-side surface 142 of the fourth lens element 140 is Y42, thefollowing condition is satisfied: Y42/Y11=0.91.

When the maximum effective radius of the inner-side surface 142 of thefourth lens element 140 is Y42, and an entrance pupil diameter of thelens system is EPD, the following condition is satisfied:(Y42×2)/EPD=1.09.

When a vertical distance between the inflection point closest to anoptical axis on the outer-side surface 121 of the second lens element120 and the optical axis is Yp21, and the focal length of the lenssystem is f, the following condition is satisfied: Yp21/f=0.09.

When a vertical distance between the inflection point closest to theoptical axis on the inner-side surface 122 of the second lens element120 and the optical axis is Yp22, and the focal length of the lenssystem is f, the following condition is satisfied: Yp22/f=0.02.

The detailed optical data of the 1st embodiment are shown in Table 1 andthe aspheric surface data are shown in Table 2 below.

TABLE 1 1st Embodiment f = 3.18 mm, Fno = 2.21, HFOV = 13.0 deg. SurfaceAbbe Focal dn/dt # Curvature Radius Thickness Material Index # Length×10⁻⁶ 0 Object Plano 500.000 1 Ape. Stop Plano 0.015 2 DOE Plano 0.122Silica 1.451 67.8 — — 3 Plano 0.015 4 Cover Glass Plano 0.223 Glass1.508 64.2 — — 5 Plano 0.080 6 Lens 1 1.100 (ASP) 0.696 Plastic 1.59426.0 1.11 −118.8 7 −1.245 (ASP) 0.093 8 Lens 2 -0.558 (ASP) 0.388Plastic 1.634 20.4 −0.90 −117.0 9 −39.375 (ASP) 0.225 10 Lens 3 0.476(ASP) 0.250 Plastic 1.626 21.5 5.19 −117.5 11 0.445 (ASP) 1.178 12 Lens4 6.343 (ASP) 0.500 Plastic 1.617 23.5 2.40 −110.0 13 −1.878 (ASP) 0.12014 Light Source Plano — Note: Reference wavelength is 940.0 nm.

TABLE 2 Aspheric Coefficients Surface # 6 7 8 9 k= −1.2550E+00−9.4133E+00 −5.2864E+00 −6.9336E+01 A4=   8.3890E−02   4.1217E−01  7.5428E−01   8.6610E−01 A6= −1.1837E−01 −1.8862E+00 −1.7874E+00−9.9840E−01 A8=   1.5791E−01   6.2597E+00   5.4005E+00   4.0762E+00 A10=−4.3886E−01 −8.3209E+00 −6.0933E+00 −1.1490E+01 A12=   1.7287E−01  3.6144E+00   2.2067E+00   1.8711E+01 Surface # 10 11 12 13 k=−1.9982E+00 −1.2984E+00 −6.6800E−02   9.0338E−01 A4= −1.9367E−01−6.3328E−01   4.1909E−02   5.8638E−03 A6= −9.0397E−01 −1.2684E+00  2.1292E−01   4.0553E−01 A8= −4.1163E+00 −2.3361E+00 −1.2023E−01−7.4961E−01 A10=   1.0128E+01   1.7356E+01   8.3341E−02   1.0856E+00Al2= −7.6227E+00 −2.0594E+01   5.7220E−02 −3.7741E−01

In Table 1, the curvature radius, the thickness and the focal length areshown in millimeters (mm). Surface numbers 0-14 represent the surfacessequentially arranged from the outer side to the inner side along theoptical axis. In Table 2, k represents the conic coefficient of theequation of the aspheric surface profiles. A4-A12 represent the asphericcoefficients ranging from the 4th order to the 12th order. The tablespresented below for each embodiment are the corresponding schematicparameter and aberration curves, and the definitions of the tables arethe same as Table 1 and Table 2 of the 1st embodiment. Therefore, anexplanation in this regard will not be provided again.

2nd Embodiment

FIG. 3 is a schematic view of a projection device according to the 2ndembodiment of the present disclosure. FIG. 4 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 2ndembodiment. In FIG. 3, the projection device includes a lens system (itsreference numeral is omitted) of the present disclosure, a light source260, a diffractive optical element 270 and a cover glass 280. The lenssystem includes, in order from an outer side to an inner side, anaperture stop 200, a first lens element 210, a second lens element 220,a third lens element 230, a fourth lens element 240 and a conjugatesurface 250. The lens system includes four lens elements (210, 220, 230and 240) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 210 with positive refractive power has anouter-side surface 211 being convex in a paraxial region thereof and aninner-side surface 212 being convex in a paraxial region thereof. Thefirst lens element 210 is made of glass material and has the outer-sidesurface 211 and the inner-side surface 212 being both aspheric. Theinner-side surface 212 of the first lens element 210 has at least oneinflection point and at least one critical point.

The second lens element 220 with negative refractive power has anouter-side surface 221 being concave in a paraxial region thereof and aninner-side surface 222 being concave in a paraxial region thereof. Thesecond lens element 220 is made of plastic material and has theouter-side surface 221 and the inner-side surface 222 being bothaspheric. Each of the outer-side surface 221 and the inner-side surface222 of the second lens element 220 has at least one inflection point.

The third lens element 230 with negative refractive power has anouter-side surface 231 being convex in a paraxial region thereof and aninner-side surface 232 being concave in a paraxial region thereof. Thethird lens element 230 is made of plastic material and has theouter-side surface 231 and the inner-side surface 232 being bothaspheric. Each of the outer-side surface 231 and the inner-side surface232 of the third lens element 230 has at least one inflection point.

The fourth lens element 240 with positive refractive power has anouter-side surface 241 being convex in a paraxial region thereof and aninner-side surface 242 being concave in a paraxial region thereof. Thefourth lens element 240 is made of plastic material and has theouter-side surface 241 and the inner-side surface 242 being bothaspheric. Each of the outer-side surface 241 and the inner-side surface242 of the fourth lens element 240 has at least one inflection point.

The light source 260 is disposed on or near the conjugate surface 250 ofthe lens system. The diffractive optical element 270 is made of silica.The diffractive optical element 270 and the cover glass 280 are locatedbetween the aperture stop 200 and the outer-side surface 211 of thefirst lens element 210, and will not affect the focal length of the lenssystem.

The detailed optical data of the 2nd embodiment are shown in Table 3 andthe aspheric surface data are shown in Table 4 below.

TABLE 3 2nd Embodiment f = 3.20 mm, Fno = 2.04, HFOV = 11.3 deg. SurfaceCurvature Abbe dn/dt # Radius Thickness Material Index # Focal ×10⁻⁶ 0Object Plano 550.000 1 Ape. Stop Plano 0.015 2 DOE Plano 0.180 Silica1.451 67.8 — — 3 Plano 0.015 4 Cover Glass Plano 0.180 Glass 1.508 64.2— — 5 Plano 0.080 6 Lens 1 1.099 (ASP) 0.907 Glass 1.508 64.2 1.64 2.7 7−2.508 (ASP) 0.357 8 Lens 2 −20.353 (ASP) 0.250 Plastic 1.641 19.5 −1.11−115.0 9 0.742 (ASP) 0.600 10 Lens 3 1.425 (ASP) 0.330 Plastic 1.64119.5 −11.08 −115.0 11 1.080 (ASP) 0.374 12 Lens 4 0.936 (ASP) 0.400Plastic 1.626 21.5 1.54 −117.5 13 27.778 (ASP) 0.135 14 Light Plano —Source Note: Reference wavelength is 940.0 nm.

TABLE 4 Aspheric Coefficients Surface # 6 7 8 9 k= −6.2196E−01−1.0556E+01   9.0000E+01   1.6668E−01 A4=   3.1623E−02   4.2819E−01  2.3144E+00   2.7379E+00 A6=   3.0799E−02 −4.4288E−01 −8.6225E+00−6.7621E+00 A8=   7.7548E−02   5.5955E−02   2.4494E+01   4.2572E+01 A10=−1.3407E−01 −1.8201E−01 −5.7401E+01 −2.2936E+02 A12=   4.8283E−02  2.5453E−01   5.1358E+01   3.2092E+02 Surface # 10 11 12 13 k=  6.9120E−02 −2.5504E+00   1.8100E−01   9.0000E+01 A4= −1.0794E+00−1.9899E+00 −3.3245E−01 −2.7306E−02 A6=   2.3106E+00   3.7354E+00−6.8095E−01   3.1734E+00 A8= −6.0639E+00 −8.6617E+00   4.0885E+00−1.2168E+01 A10=   1.0710E+01   1.2430E+01 −1.6529E+01   1.5218E+01 A12=−7.7529E+00 −7.4927E+00   1.7253E+01 −5.0918E+00

In the 2nd embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 2nd embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 3 and Table 4 asthe following values and satisfy the following conditions:

2nd Embodiment f [mm] 3.20 Σ|f/fi| 7.19 Fno 2.04 f/T34 8.55 HFOV [deg.]11.3 BL/f 0.04 λ [nm] 940.0 |R5/Y31| 1.93 Nmax 1.641 Y42/Y11 0.70 ΣVdi124.7 (Y42 × 2)/EPD 0.85 ΣCTi [mm] 1.89 Yp21/f 0.02 TD [mm] 3.22 Yp22/f0.15 Ymax [mm] 0.96 — —

3rd Embodiment

FIG. 5 is a schematic view of a projection device according to the 3rdembodiment of the present disclosure. FIG. 6 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 3rdembodiment. In FIG. 5, the projection device includes a lens system (itsreference numeral is omitted) of the present disclosure, a light source360, a diffractive optical element 370 and a cover glass 380. The lenssystem includes, in order from an outer side to an inner side, anaperture stop 300, a first lens element 310, a second lens element 320,a third lens element 330, a fourth lens element 340 and a conjugatesurface 350. The lens system includes four lens elements (310, 320, 330and 340) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 310 with positive refractive power has anouter-side surface 311 being convex in a paraxial region thereof and aninner-side surface 312 being concave in a paraxial region thereof. Thefirst lens element 310 is made of plastic material and has theouter-side surface 311 and the inner-side surface 312 being bothaspheric. The inner-side surface 312 of the first lens element 310 hasat least one inflection point and at least one critical point.

The second lens element 320 with negative refractive power has anouter-side surface 321 being convex in a paraxial region thereof and aninner-side surface 322 being concave in a paraxial region thereof. Thesecond lens element 320 is made of plastic material and has theouter-side surface 321 and the inner-side surface 322 being bothaspheric. Each of the outer-side surface 321 and the inner-side surface322 of the second lens element 320 has at least one inflection point.Each of the outer-side surface 321 and the inner-side surface 322 of thesecond lens element 320 has at least one critical point.

The third lens element 330 with positive refractive power has anouter-side surface 331 being convex in a paraxial region thereof and aninner-side surface 332 being concave in a paraxial region thereof. Thethird lens element 330 is made of plastic material and has theouter-side surface 331 and the inner-side surface 332 being bothaspheric. The outer-side surface 331 of the third lens element 330 hasat least one inflection point and at least one critical point. Theouter-side surface 331 of the third lens element 330 is cemented to theinner-side surface 322 of the second lens element 320.

The fourth lens element 340 with positive refractive power has anouter-side surface 341 being concave in a paraxial region thereof and aninner-side surface 342 being convex in a paraxial region thereof. Thefourth lens element 340 is made of plastic material and has theouter-side surface 341 and the inner-side surface 342 being bothaspheric.

The light source 360 is disposed on or near the conjugate surface 350 ofthe lens system. The diffractive optical element 370 is made of silica.The diffractive optical element 370 and the cover glass 380 are locatedbetween the aperture stop 300 and the outer-side surface 311 of thefirst lens element 310, and will not affect the focal length of the lenssystem.

The detailed optical data of the 3rd embodiment are shown in Table 5 andthe aspheric surface data are shown in Table 6 below.

TABLE 5 3rd Embodiment f = 3.37 mm, Fno = 2.27, HFOV = 10.1 deg. SurfaceAbbe Focal dn/dt # Curvature Radius Thickness Material Index # Length×10⁻⁶ 0 Object Plano 750.000 1 Ape. Stop Plano 0.019 2 DOE Plano 0.325Silica 1.451 67.8 — — 3 Plano 0.019 4 Cover Glass Plano 0.413 Glass1.508 64.2 — — 5 Plano 0.100 6 Lens 1 1.203 (ASP) 0.683 Plastic 1.61623.3 2.26 −73.3 7 6.908 (ASP) 0.063 8 Lens 2 1.772 (ASP) 0.313 Plastic1.634 20.4 −0.46 −117.0 9 0.233 (ASP) 0.013 Cement 1.477 53.2 10 Lens 30.252 (ASP) 0.568 Plastic 1.616 23.3 0.43 −73.3 11 0.740 (ASP) 0.556 12Lens 4 −2.100 (ASP) 0.921 Plastic 1.535 56.0 2.16 −106.1 13 −0.860 (ASP)0.250 14 Light Plano — Source Note: Reference wavelength is 940.0 nm.

TABLE 6 Aspheric Coefficients Surface # 6 7 8 9 k= −4.2773E−01  1.0516E+01 −2.5060E+01 −1.3012E+00 A4=   3.3649E−02   2.2401E−01  4.4862E−01   2.0387E+00 A6=   2.2413E−04 −1.5734E−01 −3.5696E−01  1.7235E+00 A8=   3.3367E−02 −3.5707E−01 −4.2475E−01 −2.6950E+01 A10=−2.6452E−02   2.6328E−01   2.1585E−01 — Surface # 10 11 12 13 k=−1.1870E+00   6.5143E−01   8.1623E+00 −5.2525E−01 A4=   2.2397E+00  4.5217E−01 −1.6541E−01 −1.0704E−01 A6=   5.6946E−01   2.1604E+00−3.6663E−01 −1.3288E−01 A8= −2.6834E+01 −1.1941E+01   9.1205E−01  9.8926E−02 A10= —   5.2836E+01 −6.6772E+00 −4.5545E−01

In the 3rd embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 3rd embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 5 and Table 6 asthe following values and satisfy the following conditions:

3rd Embodiment f [mm] 3.37 Σ|f/fi| 18.26 Fno 2.27 f/T34 6.07 HFOV [deg.]10.1 BL/f 0.07 λ [nm] 940.0 |R5/Y31| 0.47 Nmax 1.634 Y42/Y11 0.79 ΣVdi123.0 (Y42 × 2)/EPD 0.99 ΣCTi [mm] 2.48 Yp21/f 0.17 TD [mm] 3.12 Yp22/f0.12 Ymax [mm] 0.93 — —

4th Embodiment

FIG. 7 is a schematic view of a projection device according to the 4thembodiment of the present disclosure. FIG. 8 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 4thembodiment. In FIG. 7, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 460, a diffractive optical element 470 and a cover glass 480. Thelens system includes, in order from an outer side to an inner side, anaperture stop 400, a first lens element 410, a second lens element 420,a third lens element 430, a fourth lens element 440 and a conjugatesurface 450. The lens system includes four lens elements (410, 420, 430and 440) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 410 with positive refractive power has anouter-side surface 411 being convex in a paraxial region thereof and aninner-side surface 412 being convex in a paraxial region thereof. Thefirst lens element 410 is made of plastic material and has theouter-side surface 411 and the inner-side surface 412 being bothaspheric. The inner-side surface 412 of the first lens element 410 hasat least one inflection point and at least one critical point.

The second lens element 420 with negative refractive power has anouter-side surface 421 being concave in a paraxial region thereof and aninner-side surface 422 being concave in a paraxial region thereof. Thesecond lens element 420 is made of plastic material and has theouter-side surface 421 and the inner-side surface 422 being bothaspheric. The outer-side surface 421 of the second lens element 420 hasat least one inflection point and at least one critical point.

The third lens element 430 with positive refractive power has anouter-side surface 431 being convex in a paraxial region thereof and aninner-side surface 432 being concave in a paraxial region thereof. Thethird lens element 430 is made of plastic material and has theouter-side surface 431 and the inner-side surface 432 being bothaspheric. The outer-side surface 431 of the third lens element 430 hasat least one inflection point and at least one critical point.

The fourth lens element 440 with positive refractive power has anouter-side surface 441 being concave in a paraxial region thereof and aninner-side surface 442 being convex in a paraxial region thereof. Thefourth lens element 440 is made of plastic material and has theouter-side surface 441 and the inner-side surface 442 being bothaspheric.

The light source 460 is disposed on or near the conjugate surface 450 ofthe lens system. The diffractive optical element 470 is made of silica.The diffractive optical element 470 and the cover glass 480 are locatedbetween the aperture stop 400 and the outer-side surface 411 of thefirst lens element 410, and will not affect the focal length of the lenssystem.

The detailed optical data of the 4th embodiment are shown in Table 7 andthe aspheric surface data are shown in Table 8 below.

TABLE 7 4th Embodiment f = 3.24 mm, Fno = 2.27, HFOV = 10.1 deg. AbbeFocal dn/dt Surface # Curvature Radius Thickness Material Index # Length×10⁻⁶ 0 Object Plano 720.000 1 Ape. Stop Plano 0.018 2 DOE Plano 0.312Silica 1.451 67.8 — — 3 Plano 0.018 4 Cover Glass Plano 0.396 Glass1.508 64.2 — — 5 Plano 0.096 6 Lens 1 1.158 (ASP) 0.740 Plastic 1.61623.3 1.01 −73.3 7 −1.008 (ASP) 0.096 8 Lens 2 −0.846 (ASP) 0.300 Plastic1.634 20.4 −0.75 −117.0 9 1.250 (ASP) 0.319 10 Lens 3 0.611 (ASP) 0.300Plastic 1.616 23.3 11.66 −73.3 11 0.543 (ASP) 0.709 12 Lens 4 −2.847(ASP) 0.536 Plastic 1.616 23.3 2.14 −73.3 13 −0.966 (ASP) 0.240 14 LightSource Plano — Note: Reference wavelength is 940.0 nm.

TABLE 8 Aspheric Coefficients Surface # 6 7 8 9 k= −9.8211E−01−1.3406E+01 −1.3123E+01   3.0934E−01 A4=   4.6021E−02   2.7576E−01  5.8041E−01 −5.3284E−01 A6= −9.2945E−03 −1.1648E−01 −3.0638E−01  2.7730E+00 A8=   1.8658E−02   4.8126E−02   9.8237E−02 −5.7880E+00 A10=— —   1.1202E−01   4.3819E+00 Surface # 10 11 12 13 k= −3.5495E+00−2.2348E−01 −8.0775E+01 −7.0637E+00 A4= −8.6162E−02 −1.1634E+00−5.3588E−01 −1.0104E+00 A6= −3.3380E+00 −1.8105E+00   1.9814E+00  2.4379E+00 A8=   1.1925E+01   1.3649E+01 −8.0464E+00 −7.2140E+00 A10=−2.5154E+01 −3.9172E+01   2.3971E+01   1.3214E+01 A12= —   2.9825E−08−2.9047E+01 −1.0494E+01

In the 4th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 4th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 7 and Table 8 asthe following values and satisfy the following conditions:

4th Embodiment f [mm] 3.24 Σ|f/fi| 9.31 Fno 2.27 f/T34 4.57 HFOV [deg.]10.1 BL/f 0.07 λ [nm] 940.0 |R5/Y31| 1.15 Nmax 1.634 Y42/Y11 0.79 ΣVdi90.3 (Y42 × 2)/EPD 0.98 ΣCTi [mm] 1.88 Yp21/f 0.08 TD [mm] 3.00 Yp22/f —Ymax [mm] 0.89 — —

5th Embodiment

FIG. 9 is a schematic view of a projection device according to the 5thembodiment of the present disclosure. FIG. 10 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 5thembodiment. In FIG. 9, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 560, a diffractive optical element 570 and a cover glass 580. Thelens system includes, in order from an outer side to an inner side, anaperture stop 500, a first lens element 510, a second lens element 520,a third lens element 530, a fourth lens element 540 and a conjugatesurface 550. The lens system includes four lens elements (510, 520, 530and 540) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 510 with positive refractive power has anouter-side surface 511 being convex in a paraxial region thereof and aninner-side surface 512 being convex in a paraxial region thereof. Thefirst lens element 510 is made of plastic material and has theouter-side surface 511 and the inner-side surface 512 being bothaspheric. The inner-side surface 512 of the first lens element 510 hasat least one inflection point and at least one critical point.

The second lens element 520 with negative refractive power has anouter-side surface 521 being concave in a paraxial region thereof and aninner-side surface 522 being concave in a paraxial region thereof. Thesecond lens element 520 is made of plastic material and has theouter-side surface 521 and the inner-side surface 522 being bothaspheric. The outer-side surface 521 of the second lens element 520 hasat least one inflection point and at least one critical point.

The third lens element 530 with positive refractive power has anouter-side surface 531 being convex in a paraxial region thereof and aninner-side surface 532 being concave in a paraxial region thereof. Thethird lens element 530 is made of plastic material and has theouter-side surface 531 and the inner-side surface 532 being bothaspheric. The outer-side surface 531 of the third lens element 530 hasat least one inflection point and at least one critical point.

The fourth lens element 540 with positive refractive power has anouter-side surface 541 being concave in a paraxial region thereof and aninner-side surface 542 being convex in a paraxial region thereof. Thefourth lens element 540 is made of plastic material and has theouter-side surface 541 and the inner-side surface 542 being bothaspheric. The outer-side surface 541 of the fourth lens element 540 hasat least one inflection point and at least one critical point.

The light source 560 is disposed on or near the conjugate surface 550 ofthe lens system. The diffractive optical element 570 is made of silica.The diffractive optical element 570 and the cover glass 580 are locatedbetween the aperture stop 500 and the outer-side surface 511 of thefirst lens element 510, and will not affect the focal length of the lenssystem.

The detailed optical data of the 5th embodiment are shown in Table 9 andthe aspheric surface data are shown in Table 10 below.

TABLE 9 5th Embodiment f = 3.11 mm, Fno = 2.27, HFOV = 10.1 deg.Curvature Focal dn/dt Surface # Radius Thickness Material Index Abbe #Length ×10⁻⁶ 0 Object Plano 690.000 1 Ape. Stop Plano 0.017 2 DOE Plano0.299 Silica 1.451 67.8 — — 3 Plano 0.017 4 Cover Glass Plano 0.380Glass 1.508 64.2 — — 5 Plano 0.092 6 Lens 1 1.038 (ASP) 0.767 Plastic1.535 56.0 1.33 −106.1 7 −1.696 (ASP) 0.194 8 Lens 2 −1.211 (ASP) 0.288Plastic 1.634 20.4 −0.98 −117.0 9 1.396 (ASP) 0.223 10 Lens 3 0.526(ASP) 0.288 Plastic 1.634 20.4 8.23 −117.0 11 0.461 (ASP) 0.584 12 Lens4 −2.922 (ASP) 0.532 Plastic 1.634 20.4 1.89 −117.0 13 −0.910 (ASP)0.230 14 Light Source Plano — Note: Reference wavelength is 940.0 nm.

TABLE 10 Aspheric Coefficients Surface # 6 7 8 9 k= −7.8861E−01−2.5415E+01 −2.2941E+01   1.9982E+00 A4=   5.3901E−02   2.1431E−01  5.6531E−01 −8.4112E−01 A6=   1.1808E−02 −2.1991E−01 −6.2335E−01  3.9270E+00 A8= —   1.3024E−01   6.4813E−01 −1.0189E+01 A10= — — —  1.3926E+01 Surface # 10 11 12 13 k= −3.2627E+00 −3.3468E−01−5.2473E+01 −4.3942E+00 A4= −2.3848E−01 −1.6531E+00 −2.2213E−01−7.1851E−01 A6= −6.7927E+00 −6.5937E+00   5.5467E−01   8.9082E−01 A8=  1.8259E+01   3.5244E+01 −3.6144E−01 −1.8097E+00 A10= −2.2727E+01−6.8566E+01   5.2620E+00   2.5076E+00 A12= — — −7.0839E+00 −6.6706E−01

In the 5th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 5th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 9 and Table 10as the following values and satisfy the following conditions:

5th Embodiment f [mm] 3.11 Σ|f/fi| 7.51 Fno 2.27 f/T34 5.32 HFOV [deg.]10.1 BL/f 0.07 λ [nm] 940.0 |R5/Y31| 1.07 Nmax 1.634 Y42/Y11 0.78 ΣVdi117.2 (Y42 × 2)/EPD 0.98 ΣCTi [mm] 1.87 Yp21/f 0.08 TD [mm] 2.88 Yp22/f— Ymax [mm] 0.86 — —

6th Embodiment

FIG. 11 is a schematic view of a projection device according to the 6thembodiment of the present disclosure. FIG. 12 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 6thembodiment. In FIG. 11, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 660, a diffractive optical element 670 and a cover glass 680. Thelens system includes, in order from an outer side to an inner side, anaperture stop 600, a first lens element 610, a second lens element 620,a third lens element 630, a fourth lens element 640 and a conjugatesurface 650. The lens system includes four lens elements (610, 620, 630and 640) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 610 with positive refractive power has anouter-side surface 611 being convex in a paraxial region thereof and aninner-side surface 612 being convex in a paraxial region thereof. Thefirst lens element 610 is made of glass material and has the outer-sidesurface 611 and the inner-side surface 612 being both aspheric. Each ofthe outer-side surface 611 and the inner-side surface 612 of the firstlens element 610 has at least one inflection point. The inner-sidesurface 612 of the first lens element 610 has at least one criticalpoint.

The second lens element 620 with negative refractive power has anouter-side surface 621 being concave in a paraxial region thereof and aninner-side surface 622 being concave in a paraxial region thereof. Thesecond lens element 620 is made of plastic material and has theouter-side surface 621 and the inner-side surface 622 being bothaspheric. The outer-side surface 621 of the second lens element 620 hasat least one inflection point and at least one critical point.

The third lens element 630 with positive refractive power has anouter-side surface 631 being convex in a paraxial region thereof and aninner-side surface 632 being concave in a paraxial region thereof. Thethird lens element 630 is made of plastic material and has theouter-side surface 631 and the inner-side surface 632 being bothaspheric. Each of the outer-side surface 631 and the inner-side surface632 of the third lens element 630 has at least one inflection point.Each of the outer-side surface 631 and the inner-side surface 632 of thethird lens element 630 has at least one critical point.

The fourth lens element 640 with positive refractive power has anouter-side surface 641 being convex in a paraxial region thereof and aninner-side surface 642 being concave in a paraxial region thereof. Thefourth lens element 640 is made of plastic material and has theouter-side surface 641 and the inner-side surface 642 being bothaspheric.

The light source 660 is disposed on or near the conjugate surface 650 ofthe lens system. The diffractive optical element 670 is made of silica.The diffractive optical element 670 and the cover glass 680 are locatedbetween the aperture stop 600 and the outer-side surface 611 of thefirst lens element 610, and will not affect the focal length of the lenssystem.

The detailed optical data of the 6th embodiment are shown in Table 11and the aspheric surface data are shown in Table 12 below.

TABLE 11 6th Embodiment f = 3.20 mm, Fno = 2.05, HFOV = 10.8 deg. Focaldn/dt Surface # Curvature Radius Thickness Material Index Abbe # Length×10⁻⁶ 0 Object Plano 550.000 1 Ape. Stop Plano 0.015 2 DOE Plano 0.220Silica 1.451 67.8 — — 3 Plano 0.015 4 Cover Glass Plano 0.260 Glass1.508 64.2 — — 5 Plano 0.080 6 Lens 1 1.057 (ASP) 0.959 Glass 1.508 64.21.14 2.7 7 −0.899 (ASP) 0.092 8 Lens 2 −0.595 (ASP) 0.250 Plastic 1.64119.5 −0.68 −115.0 9 1.899 (ASP) 0.289 10 Lens 3 0.447 (ASP) 0.254Plastic 1.641 19.5 2.48 −115.0 11 0.484 (ASP) 1.225 12 Lens 4 1.385(ASP) 0.467 Plastic 1.617 23.5 2.35 −110.0 13 27.778 (ASP) 0.164 14Light Source Plano — Note: Reference wavelength is 940.0 nm.

TABLE 12 Aspheric Coefficients Surface # 6 7 8 9 k= −7.4337E−01−1.3111E+01 −7.9561E+00   7.6241E+00 A4=   5.3645E−02   3.8447E−01  8.3547E−01 −1.5941E−01 A6= −1.9354E−02 −6.5176E−01 −1.2477E+00  3.7002E+00 A8=   5.2018E−02   1.9346E+00   2.4527E+00 −1.2923E+01 A10=−1.6548E−02 −2.9764E+00 −2.2312E+00   2.5889E+01 A12= −4.6194E−02  1.4178E+00   3.9369E−01 −8.6761E+00 Surface # 10 11 12 13 k=−2.0558E+00 −1.4980E+00   1.7316E+00   9.0000E+01 A4= −4.7383E−01−9.1475E−01   5.6560E−02   2.3897E−01 A6= −3.0976E−01 −2.1505E+00  2.9350E−01   4.7576E−01 A8= −6.0844E+00   7.1160E+00 −8.2575E−01  8.5994E−01 A10=   2.1534E+01 −7.1354E+00   1.1798E+00 −5.0063E+00 A12=−2.0674E+01   8.0075E−01 −4.9762E−01   9.7177E+00

In the 6th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 6th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 11 and Table 12as the following values and satisfy the following conditions:

6th Embodiment f [mm] 3.20 Σ|f/fi| 10.15 Fno 2.05 f/T34 2.61 HFOV [deg.]10.8 BL/f 0.05 λ [nm] 940.0 |R5/Y31| 0.67 Nmax 1.641 Y42/Y11 0.66 ΣVdi126.7 (Y42 × 2)/EPD 0.81 ΣCTi [mm] 1.93 Yp21/f 0.08 TD [mm] 3.54 Yp22/f— Ymax [mm] 0.96 — —

7th Embodiment

FIG. 13 is a schematic view of a projection device according to the 7thembodiment of the present disclosure. FIG. 14 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 7thembodiment. In FIG. 13, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 760, a diffractive optical element 770 and a cover glass 780. Thelens system includes, in order from an outer side to an inner side, anaperture stop 700, a first lens element 710, a second lens element 720,a third lens element 730, a fourth lens element 740 and a conjugatesurface 750. The lens system includes four lens elements (710, 720, 730and 740) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 710 with positive refractive power has anouter-side surface 711 being convex in a paraxial region thereof and aninner-side surface 712 being convex in a paraxial region thereof. Thefirst lens element 710 is made of plastic material and has theouter-side surface 711 and the inner-side surface 712 being bothaspheric. Each of the outer-side surface 711 and the inner-side surface712 of the first lens element 710 has at least one inflection point. Theinner-side surface 712 of the first lens element 710 has at least onecritical point.

The second lens element 720 with negative refractive power has anouter-side surface 721 being concave in a paraxial region thereof and aninner-side surface 722 being concave in a paraxial region thereof. Thesecond lens element 720 is made of plastic material and has theouter-side surface 721 and the inner-side surface 722 being bothaspheric. The outer-side surface 721 of the second lens element 720 hasat least one inflection point and at least one critical point.

The third lens element 730 with positive refractive power has anouter-side surface 731 being convex in a paraxial region thereof and aninner-side surface 732 being concave in a paraxial region thereof. Thethird lens element 730 is made of plastic material and has theouter-side surface 731 and the inner-side surface 732 being bothaspheric. The outer-side surface 731 of the third lens element 730 hasat least one inflection point and at least one critical point.

The fourth lens element 740 with positive refractive power has anouter-side surface 741 being concave in a paraxial region thereof and aninner-side surface 742 being convex in a paraxial region thereof. Thefourth lens element 740 is made of glass material and has the outer-sidesurface 741 and the inner-side surface 742 being both aspheric. Each ofthe outer-side surface 741 and the inner-side surface 742 of the fourthlens element 740 has at least one inflection point. The outer-sidesurface 741 of the fourth lens element 740 has at least one criticalpoint.

The light source 760 is disposed on or near the conjugate surface 750 ofthe lens system. The diffractive optical element 770 is made of silica.The diffractive optical element 770 and the cover glass 780 are locatedbetween the aperture stop 700 and the outer-side surface 711 of thefirst lens element 710, and will not affect the focal length of the lenssystem.

The detailed optical data of the 7th embodiment are shown in Table 13and the aspheric surface data are shown in Table 14 below.

TABLE 13 7th Embodiment f = 3.25 mm, Fno = 2.08, HFOV = 10.5 deg.Curvature Focal dn/dt Surface # Radius Thickness Material Index Abbe #Length ×10⁻⁶ 0 Object Plano 650.000 1 Ape. Stop Plano 0.015 2 DOE Plano0.200 Silica 1.451 67.8 — — 3 Plano 0.015 4 Cover Glass Plano 0.200Glass 1.508 64.2 — — 5 Plano 0.080 6 Lens 1 1.135 (ASP) 0.800 Plastic1.553 37.4 1.11 −95.0 7 −1.001 (ASP) 0.104 8 Lens 2 −0.933 (ASP) 0.544Plastic 1.641 19.5 −0.77 −115.0 9 1.297 (ASP) 0.133 10 Lens 3 0.459(ASP) 0.250 Plastic 1.641 19.5 8.37 −115.0 11 0.395 (ASP) 0.760 12 Lens4 −5.908 (ASP) 0.509 Glass 1.604 36.3 1.87 2.1 13 −0.981 (ASP) 0.080 14Light Source Plano — Note: Reference wavelength is 940.0 nm.

TABLE 14 Aspheric Coefficients Surface # 6 7 8 9 k= −1.6871E−01−1.4072E+01 −1.7269E+01   2.7212E+00 A4= −2.4569E−02   2.9729E−01  6.1961E−01 −1.4045E+00 A6= −4.5758E−02 −4.5765E−01 −1.1603E+00  4.9087E+00 A8=   3.2996E−02   2.0886E−01   1.7995E+00 −1.3111E+01 A10=−1.4079E−01   4.0805E−01 −7.7663E−01   1.9773E+01 A12=   6.0571E−02−3.5707E−01 — — Surface # 10 11 12 13 k= −3.2748E+00 −5.0369E−01−4.5421E−01 −2.2334E+00 A4=   2.3407E−01 −1.9303E+00   1.2182E−01−2.3588E−01 A6= −1.2495E+01 −1.1503E+01 −1.2631E−01 −1.0495E−01 A8=  4.2121E+01   6.5806E+01   1.7378E+00   1.2160E+00 A10= −5.0937E+01−1.4202E+02 −9.0700E−01 −3.0406E+00 A12= — — −2.2676E−01   5.0434E+00

In the 7th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 7th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 13 and Table 14as the following values and satisfy the following conditions:

7th Embodiment f [mm] 3.25 Σ|f/fi| 9.25 Fno 2.08 f/T34 4.28 HFOV [deg.]10.5 BL/f 0.02 λ [nm] 940.0 |R5/Y31| 0.89 Nmax 1.641 Y42/Y11 0.73 ΣVdi112.7 (Y42 × 2)/EPD 0.87 ΣCTi [mm] 2.10 Yp21/f 0.08 TD [mm] 3.10 Yp22/f— Ymax [mm] 0.92 — —

8th Embodiment

FIG. 15 is a schematic view of a projection device according to the 8thembodiment of the present disclosure. FIG. 16 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 8thembodiment. In FIG. 15, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 860, a diffractive optical element 870 and a cover glass 880. Thelens system includes, in order from an outer side to an inner side, anaperture stop 800, a first lens element 810, a second lens element 820,a third lens element 830, a fourth lens element 840 and a conjugatesurface 850. The lens system includes four lens elements (810, 820, 830and 840) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 810 with positive refractive power has anouter-side surface 811 being convex in a paraxial region thereof and aninner-side surface 812 being convex in a paraxial region thereof. Thefirst lens element 810 is made of plastic material and has theouter-side surface 811 and the inner-side surface 812 being bothaspheric. Each of the outer-side surface 811 and the inner-side surface812 of the first lens element 810 has at least one inflection point. Theinner-side surface 812 of the first lens element 810 has at least onecritical point.

The second lens element 820 with negative refractive power has anouter-side surface 821 being concave in a paraxial region thereof and aninner-side surface 822 being convex in a paraxial region thereof. Thesecond lens element 820 is made of plastic material and has theouter-side surface 821 and the inner-side surface 822 being bothaspheric. Each of the outer-side surface 821 and the inner-side surface822 of the second lens element 820 has at least one inflection point.Each of the outer-side surface 821 and the inner-side surface 822 of thesecond lens element 820 has at least one critical point.

The third lens element 830 with positive refractive power has anouter-side surface 831 being convex in a paraxial region thereof and aninner-side surface 832 being concave in a paraxial region thereof. Thethird lens element 830 is made of plastic material and has theouter-side surface 831 and the inner-side surface 832 being bothaspheric. Each of the outer-side surface 831 and the inner-side surface832 of the third lens element 830 has at least one inflection point. Theouter-side surface 831 of the third lens element 830 has at least onecritical point.

The fourth lens element 840 with positive refractive power has anouter-side surface 841 being concave in a paraxial region thereof and aninner-side surface 842 being convex in a paraxial region thereof. Thefourth lens element 840 is made of plastic material and has theouter-side surface 841 and the inner-side surface 842 being bothaspheric. The outer-side surface 841 of the fourth lens element 840 hasat least one inflection point and at least one critical point.

The light source 860 is disposed on or near the conjugate surface 850 ofthe lens system. The diffractive optical element 870 is made of silica.The diffractive optical element 870 and the cover glass 880 are locatedbetween the aperture stop 800 and the outer-side surface 811 of thefirst lens element 810, and will not affect the focal length of the lenssystem.

The detailed optical data of the 8th embodiment are shown in Table 15and the aspheric surface data are shown in Table 16 below.

TABLE 15 8th Embodiment f = 3.16 mm, Fno = 2.17, HFOV = 13.2 deg.Curvature Focal dn/dt Surface # Radius Thickness Material Index Abbe #Length ×10⁻⁶ 0 Object Plano 500.000 1 Ape. Stop Plano 0.015 2 DOE Plano0.237 Silica 1.451 67.8 — — 3 Plano 0.015 4 Cover Glass Plano 0.299Glass 1.508 64.2 — — 5 Plano 0.080 6 Lens 1 1.100 (ASP) 0.678 Plastic1.594 26.0 1.18 −118.8 7 −1.485 (ASP) 0.099 8 Lens 2 −0.567 (ASP) 0.289Plastic 1.634 20.4 −0.97 −117.0 9 −9.008 (ASP) 0.098 10 Lens 3 0.488(ASP) 0.250 Plastic 1.626 21.5 4.32 −117.5 11 0.477 (ASP) 1.237 12 Lens4 −11.866 (ASP) 0.500 Plastic 1.617 23.5 2.60 −110.0 13 −1.434 (ASP)0.122 14 Light Source Plano — Note: Reference wavelength is 940.0 nm.

TABLE 16 Aspheric Coefficients Surface # 6 7 8 9 k= −1.2584E+00−7.8209E+00 −6.5102E+00   6.5785E+01 A4=   8.9348E−02   3.7559E−01  6.6367E−01   1.3676E+00 A6= −2.0224E−01 −2.1187E+00 −2.0129E+00−6.4244E+00 A8=   4.0191E−01   6.9509E+00   7.2273E+00   2.8473E+01 A10=−8.9318E−01 −8.6450E+00 −9.0508E+00 −6.5896E+01 A12=   5.5802E−01  3.6031E+00   4.1968E+00   6.6661E+01 Surface # 10 11 12 13 k=−1.9532E+00 −9.8420E−01 −9.9000E+01   1.1995E+00 A4=   5.2032E−03  3.4650E−01 −9.2676E−02 −1.7465E−01 A6= −1.9039E+00 −6.8890E+00  8.0382E−01   1.4557E+00 A8= −3.9046E−01   1.7603E+01 −2.5620E+00−4.0995E+00 A10=   4.1296E+00 −1.9328E+01   4.4182E+00   6.0368E+00 A12=−4.3081E+00   4.2202E+00 −2.8376E+00 −3.2081E+00

In the 8th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 8th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 15 and Table 16as the following values and satisfy the following conditions:

8th Embodiment f [mm] 3.16 Σ|f/fi| 7.90 Fno 2.17 f/T34 2.56 HFOV [deg.]13.2 BL/f 0.04 λ [nm] 940.0 |R5/Y31| 0.77 Nmax 1.634 Y42/Y11 0.90 ΣVdi91.4 (Y42 × 2)/EPD 1.13 ΣCTi [mm] 1.72 Yp21/f 0.09 TD [mm] 3.15 Yp22/f0.03 Ymax [mm] 0.92 — —

9th Embodiment

FIG. 17 is a schematic view of a projection device according to the 9thembodiment of the present disclosure. FIG. 18 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 9thembodiment. In FIG. 17, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 960, a diffractive optical element 970 and a cover glass 980. Thelens system includes, in order from an outer side to an inner side, anaperture stop 900, a first lens element 910, a second lens element 920,a third lens element 930, a fourth lens element 940 and a conjugatesurface 950. The lens system includes four lens elements (910, 920, 930and 940) with no additional lens element disposed between each of theadjacent four lens elements.

The first lens element 910 with positive refractive power has anouter-side surface 911 being convex in a paraxial region thereof and aninner-side surface 912 being concave in a paraxial region thereof. Thefirst lens element 910 is made of glass material and has the outer-sidesurface 911 and the inner-side surface 912 being both spherical.

The second lens element 920 with negative refractive power has anouter-side surface 921 being convex in a paraxial region thereof and aninner-side surface 922 being concave in a paraxial region thereof. Thesecond lens element 920 is made of plastic material and has theouter-side surface 921 and the inner-side surface 922 being bothaspheric. The inner-side surface 922 of the second lens element 920 hasat least one inflection point.

The third lens element 930 with negative refractive power has anouter-side surface 931 being concave in a paraxial region thereof and aninner-side surface 932 being convex in a paraxial region thereof. Thethird lens element 930 is made of plastic material and has theouter-side surface 931 and the inner-side surface 932 being bothaspheric. The inner-side surface 932 of the third lens element 930 hasat least one inflection point and at least one critical point.

The fourth lens element 940 with positive refractive power has anouter-side surface 941 being concave in a paraxial region thereof and aninner-side surface 942 being convex in a paraxial region thereof. Thefourth lens element 940 is made of plastic material and has theouter-side surface 941 and the inner-side surface 942 being bothaspheric. Each of the outer-side surface 941 and the inner-side surface942 of the fourth lens element 940 has at least one inflection point.The outer-side surface 941 of the fourth lens element 940 has at leastone critical point.

The light source 960 is disposed on or near the conjugate surface 950 ofthe lens system. The diffractive optical element 970 is made of silica.The diffractive optical element 970 and the cover glass 980 are locatedbetween the aperture stop 900 and the outer-side surface 911 of thefirst lens element 910, and will not affect the focal length of the lenssystem.

The detailed optical data of the 9th embodiment are shown in Table 17and the aspheric surface data are shown in Table 18 below.

TABLE 17 9th Embodiment f = 3.29 mm, Fno = 2.27, HFOV = 10.5 deg.Curvature Focal dn/dt Surface # Radius Thickness Material Index Abbe #Length ×10⁻⁶ 0 Object Plano 732.000 1 Ape. Stop Plano 0.018 2 DOE Plano0.317 Silica 1.451 67.8 — — 3 Plano 0.018 4 Cover Glass Plano 0.403Glass 1.508 64.2 — — 5 Plano 0.098 6 Lens 1 1.964 0.756 Glass 1.966 25.53.01 3.2 7 4.912 0.037 8 Lens 2 0.793 (ASP) 0.382 Plastic 1.634 20.4−20.41 −117.0 9 0.608 (ASP) 0.744 10 Lens 3 −1.130 (ASP) 0.244 Plastic1.634 20.4 −10.14 −117.0 11 −1.487 (ASP) 0.276 12 Lens 4 −1.465 (ASP)0.611 Plastic 1.535 56.0 2.65 −106.1 13 −0.826 (ASP) 0.244 14 LightSource Plano — Note: Reference wavelength is 940.0 nm.

TABLE 18 Aspheric Coefficients Surface # 8 9 10 k= −5.6540E−01−1.1175E+00 −1.3184E−01 A4=   9.7911E−02   4.8580E−01   2.4863E−01 A6=  4.6181E−02 −7.3103E−02 −2.2242E+00 A8=   2.2083E−01   1.9935E+00  2.0679E+01 A10= −2.7401E−01 −7.2919E+00 −1.1574E+02 A12=   7.7990E−02−4.1882E+00   9.6932E+01 Surface # 11 12 13 k= −3.0284E+01   1.8945E+00−5.9682E−02 A4= −6.4304E−02   6.3669E−01   1.1271E−01 A6=   5.2059E+00−8.7510E−01 −4.3700E−01 A8= −7.9275E+00   8.2904E+00   1.9741E+00 A10=  1.8318E+01 −1.6693E+01 −3.4329E+00 A12= −5.3225E+01   1.0725E+01  4.0270E+00

In the 9th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 9th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 17 and Table 18as the following values and satisfy the following conditions:

9th Embodiment f [mm] 3.29 E|f/fi| 2.82 Fno 2.27 f/T34 11.93 HFOV [deg.]10.5 BL/f 0.07 λ [nm] 940.0 |R5/Y31| 2.40 Nmax 1.966 Y42/Y11 0.83 ΣVdi122.3 (Y42 × 2)/EPD 1.01 ΣCTi [mm] 1.99 Yp21/f — TD [mm] 3.05 Yp22/f0.16 Ymax [mm] 0.88 — —

10th Embodiment

FIG. 19 is a schematic view of a projection device according to the 10thembodiment of the present disclosure. FIG. 20 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 10thembodiment. In FIG. 19, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 1060, a diffractive optical element 1070 and a cover glass 1080.The lens system includes, in order from an outer side to an inner side,an aperture stop 1000, a first lens element 1010, a second lens element1020, a third lens element 1030, a fourth lens element 1040 and aconjugate surface 1050. The lens system includes four lens elements(1010, 1020, 1030 and 1040) with no additional lens element disposedbetween each of the adjacent four lens elements.

The first lens element 1010 with positive refractive power has anouter-side surface 1011 being convex in a paraxial region thereof and aninner-side surface 1012 being concave in a paraxial region thereof. Thefirst lens element 1010 is made of glass material and has the outer-sidesurface 1011 and the inner-side surface 1012 being both spherical.

The second lens element 1020 with negative refractive power has anouter-side surface 1021 being convex in a paraxial region thereof and aninner-side surface 1022 being concave in a paraxial region thereof. Thesecond lens element 1020 is made of plastic material and has theouter-side surface 1021 and the inner-side surface 1022 being bothaspheric.

The third lens element 1030 with negative refractive power has anouter-side surface 1031 being concave in a paraxial region thereof andan inner-side surface 1032 being convex in a paraxial region thereof.The third lens element 1030 is made of plastic material and has theouter-side surface 1031 and the inner-side surface 1032 being bothaspheric. The inner-side surface 1032 of the third lens element 1030 hasat least one inflection point and at least one critical point.

The fourth lens element 1040 with positive refractive power has anouter-side surface 1041 being concave in a paraxial region thereof andan inner-side surface 1042 being convex in a paraxial region thereof.The fourth lens element 1040 is made of plastic material and has theouter-side surface 1041 and the inner-side surface 1042 being bothaspheric. Each of the outer-side surface 1041 and the inner-side surface1042 of the fourth lens element 1040 has at least one inflection point.The outer-side surface 1041 of the fourth lens element 1040 has at leastone critical point.

The light source 1060 is disposed on or near the conjugate surface 1050of the lens system. The diffractive optical element 1070 is made ofsilica. The diffractive optical element 1070 and the cover glass 1080are located between the aperture stop 1000 and the outer-side surface1011 of the first lens element 1010, and will not affect the focallength of the lens system.

The detailed optical data of the 10th embodiment are shown in Table 19and the aspheric surface data are shown in Table 20 below.

TABLE 19 10th Embodiment f = 3.40 mm, Fno = 2.27, HFOV = 10.5 deg.Curvature Focal dn/dt Surface # Radius Thickness Material Index Abbe #Length ×10⁻⁶ 0 Object Plano 756.000 1 Ape. Stop Plano 0.019 2 DOE Plano0.328 Silica 1.451 67.8 — — 3 Plano 0.019 4 Cover Glass Plano 0.416Glass 1.508 64.2 — — 5 Plano 0.101 6 Lens 1 1.891 0.756 Glass 1.966 25.52.85 3.2 7 4.850 0.063 8 Lens 2 0.842 (ASP) 0.410 Plastic 1.634 20.4−6.81 −117.0 9 0.572 (ASP) 0.747 10 Lens 3 −1.896 (ASP) 0.265 Plastic1.634 20.4 −24.80 −117.0 11 −2.272 (ASP) 0.278 12 Lens 4 −1.704 (ASP)0.631 Plastic 1.535 56.0 2.72 −106.1 13 −0.886 (ASP) 0.252 14 LightSource Plano — Note: Reference wavelength is 940.0 nm.

TABLE 20 Aspheric Coefficients Surface # 8 9 10 k= −7.6922E−01−9.7888E−01   3.6951E−01 A4=   8.9115E−02   4.1375E−01   1.2575E−01 A6=  1.0811E−01   3.9869E−01 −9.1451E−01 A8= −1.9393E−01 −4.1744E−01  5.8024E+00 A10=   1.4034E−01 −2.8902E+00 −3.4377E+01 Surface # 11 1213 k=   4.4648E+00   1.2831E+00   6.2063E−03 A4=   8.2668E−01  4.7084E−01   4.9560E−02 A6= −3.9448E−01 −4.2016E−01   8.7141E−02 A8=  1.1866E+01   5.5071E+00 −4.1080E−02 A10= −3.8721E+01 −1.1334E+01  3.7008E−01 A12=   2.8948E+01   7.0299E+00   8.4198E−01

In the 10th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 10th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 19 and Table 20as the following values and satisfy the following conditions:

10th Embodiment f [mm] 3.40 Σ|f/fi| 3.08 Fno 2.27 f/T34 12.20 HFOV[deg.] 10.5 BL/f 0.07 λ [nm] 940.0 |R5/Y31| 3.75 Nmax 1.966 Y42/Y11 0.83ΣVdi 122.3 (Y42 × 2)/EPD 1.01 ΣCTi [mm] 2.06 Yp21/f — TD [mm] 3.15Yp22/f — Ymax [mm] 0.91 — —

11th Embodiment

FIG. 21 is a schematic view of a projection device according to the 11thembodiment of the present disclosure. FIG. 22 shows, in order from leftto right, spherical aberration curves, astigmatic field curves and adistortion curve of the projection device according to the 11thembodiment. In FIG. 21, the projection device includes the lens system(its reference numeral is omitted) of the present disclosure, a lightsource 1160, a diffractive optical element 1170 and a cover glass 1180.The lens system includes, in order from an outer side to an inner side,an aperture stop 1100, a first lens element 1110, a second lens element1120, a third lens element 1130, a fourth lens element 1140 and aconjugate surface 1150. The lens system includes four lens elements(1110, 1120, 1130 and 1140) with no additional lens element disposedbetween each of the adjacent four lens elements.

The first lens element 1110 with positive refractive power has anouter-side surface 1111 being convex in a paraxial region thereof and aninner-side surface 1112 being concave in a paraxial region thereof. Thefirst lens element 1110 is made of glass material and has the outer-sidesurface 1111 and the inner-side surface 1112 being both spherical.

The second lens element 1120 with positive refractive power has anouter-side surface 1121 being convex in a paraxial region thereof and aninner-side surface 1122 being concave in a paraxial region thereof. Thesecond lens element 1120 is made of plastic material and has theouter-side surface 1121 and the inner-side surface 1122 being bothaspheric. The inner-side surface 1122 of the second lens element 1120has at least one inflection point.

The third lens element 1130 with negative refractive power has anouter-side surface 1131 being concave in a paraxial region thereof andan inner-side surface 1132 being convex in a paraxial region thereof.The third lens element 1130 is made of plastic material and has theouter-side surface 1131 and the inner-side surface 1132 being bothaspheric. The inner-side surface 1132 of the third lens element 1130 hasat least one inflection point and at least one critical point.

The fourth lens element 1140 with positive refractive power has anouter-side surface 1141 being concave in a paraxial region thereof andan inner-side surface 1142 being convex in a paraxial region thereof.The fourth lens element 1140 is made of plastic material and has theouter-side surface 1141 and the inner-side surface 1142 being bothaspheric. Each of the outer-side surface 1141 and the inner-side surface1142 of the fourth lens element 1140 has at least one inflection point.The outer-side surface 1141 of the fourth lens element 1140 has at leastone critical point.

The light source 1160 is disposed on or near the conjugate surface 1150of the lens system. The diffractive optical element 1170 is made ofsilica. The diffractive optical element 1170 and the cover glass 1180are located between the aperture stop 1100 and the outer-side surface1111 of the first lens element 1110, and will not affect the focallength of the lens system.

The detailed optical data of the 11th embodiment are shown in Table 21and the aspheric surface data are shown in Table 22 below.

TABLE 21 11th Embodiment f = 3.51 mm, Fno = 2.27, HFOV = 10.1 deg.Curvature Abbe Focal dn/dt Surface # Radius Thickness Material Index #Length ×10⁻⁶ 0 Object Plano 780.000 1 Ape. Stop Plano 0.020 2 DOE Plano0.338 Silica 1.451 67.8 — — 3 Plano 0.020 4 Cover Glass Plano 0.429Glass 1.508 64.2 — — 5 Plano 0.104 6 Lens 1 2.470 0.780 Glass 1.966 25.53.39 3.2 7 8.444 0.039 8 Lens 2 0.893 (ASP) 0.462 Plastic 1.634 20.4105.72 −117.0 9 0.724 (ASP) 0.710 10 Lens 3 −1.442 (ASP) 0.260 Plastic1.634 20.4 −5.85 −117.0 11 −2.525 (ASP) 0.410 12 Lens 4 −1.396 (ASP)0.590 Plastic 1.634 20.4 2.65 −117.0 13 −0.888 (ASP) 0.260 14 LightSource Plano — Note: Reference wavelength is 940.0 nm.

TABLE 22 Aspheric Coefficients Surface # 8 9 10 k= −7.4042E−01−1.2715E+00   1.7560E+00 A4=   8.8605E−02   2.7277E−01   3.6057E−01 A6=  5.1599E−02 −5.1685E−01 −1.1735E+00 A8= −4.1526E−02   2.0548E+00  1.0126E+01 A10=   1.2006E−01 −1.0372E+01 −8.3069E+01 A12= −1.9812E−01  1.0396E+01   1.4602E+02 Surface # 11 12 13 k= −9.9000E+01 −1.5505E−01−6.1244E−01 A4=   2.0717E−01   2.0516E−01 −2.9840E−02 A6=   5.3062E+00  5.4615E−01 −4.7154E−01 A8= −1.4663E+01   2.3283E−01   2.0970E+00 A10=  3.3331E+01 −5.9584E−01 −4.1350E+00 A12= −2.6725E+01   1.1704E−02  3.0392E+00

In the 11th embodiment, the equation of the aspheric surface profiles ofthe aforementioned lens elements is the same as the equation of the 1stembodiment. Also, the definitions of these parameters shown in thefollowing table are the same as those stated in the 1st embodiment withcorresponding values for the 11th embodiment, so an explanation in thisregard will not be provided again.

Moreover, these parameters can be calculated from Table 21 and Table 22as the following values and satisfy the following conditions:

11th Embodiment f [mm] 3.51 Σ|f/fi| 2.99 Fno 2.27 f/T34 8.56 HFOV [deg.]10.1 BL/f 0.07 λ [nm] 940.0 |R5/Y31| 2.87 Nmax 1.966 Y42/Y11 0.83 ΣVdi86.7 (Y42 × 2)/EPD 0.99 ΣCTi [mm] 2.09 Yp21/f — TD [mm] 3.25 Yp22/f 0.15Ymax [mm] 0.92 — —

12th Embodiment

FIG. 23 is a schematic view of a detecting module according to the 12thembodiment of the present disclosure. In this embodiment, a detectingmodule 10 includes a receiving device 11 and a projection device 12disclosed in the first embodiment. The receiving device 11 includes animaging lens assembly 11 a and an image sensor 11 b.

The projection device 12 includes a lens system 12 a and a light source160 featuring with high directional characteristic (low divergence) andhigh intensity. The light source 160 can be a laser, a superluminescentdiode (SLED), a micro LED, a resonant cavity light emitting diode(RCLED), a VCSEL and the like. The light source 160 can be a singlelight source or multiple light sources disposed on the conjugate surface150 on the inner side of the lens system 12 a to present good projectionquality. In a case that the light source 160 of the projection device 12is a VCSEL disposed on the conjugate surface 150, the light source 160is favorable for the projection device 12 emitting high directionallight rays having low divergence and high intensity so as to enhance theilluminance of the conjugate surface on an outer side of the lens system12 a. The light source 160 of the projection device 12 projects a lightonto a detected object O. The detected object O reflects the light, andthe reflected light travels into the receiving device 11. The lighttraveling into the receiving device 11 passes through the imaging lensassembly 11 a and then is incident on the image sensor 11 b.

The diffractive optical element 170 of the projection device 12 helpsproject the light evenly onto the detected object O, or helps diffractthe light to enlarge the projection angle and the projection field. Thediffractive optical element 170 can be a diffuser, a raster or acombination thereof (but not limited thereto). The diffractive opticalelement 170 can have a micro structure such as a diffraction grating forscattering the light and replicating a speckle pattern generated by thescattered light, thereby enlarging the projection angle.

The present disclosure is not limited to the detecting module 10 in FIG.23. For example, the detecting module can include a focusing system or afocusing lens assembly. The focusing system is configured to adjust thefocal lengths of the lens system 12 a and the imaging lens assembly 11 aaccording to different photographing conditions so as to provide highimage resolution. The detecting module can include a lens assembly withreflection functionality in order to reduce the size of the detectingmodule, thereby improving the space utilization.

13th Embodiment

FIG. 24 is a schematic view of an electronic device according to the13th embodiment of the present disclosure. FIG. 25 is a schematic viewof the detection of a 3D facial profile by using the electronic devicein FIG. 24. In this embodiment, an electronic device 20 is a smartphoneincluding an image capturing unit 21, an image signal processor 22 andthe detecting module 10 disclosed in the 12th embodiment. The imagecapturing unit 21 can include a conventional photographing lensassembly.

A laser array 12 b 1 is used as the light source 160 of projectiondevice 12 of the detecting module 10 in order to form specific lightpatterns. In detail, the light passes through the lens system 12 a ofthe projection device 12 to generate structured light, which isprojected onto a human face (the detected object O). The structuredlight can be in the shape of dots, spots or stripes, but the presentdisclosure is not limited thereto. The structured light projected ontothe human face generates a 3D face structure O″ corresponding to thefacial surface of the human subject.

The imaging lens assembly 11 a of the receiving device 11 receives thelight (the 3D face structure O″) reflected off the subject's face, andprojected on the image sensor 11 b to generate a corresponding image.The image signal processor 22 is configured to analyze information ofthe image to obtain a relative distance between different parts of thesubject's face, thereby determining a 3D profile of the subject's face.Moreover, after the information of the image is analyzed by the imagesignal processor 22, an analyzed human facial image can be displayed ona screen 23 of the electronic device 20.

In FIG. 24, the detecting module 10, the image capturing unit 21 and thescreen 23 are arranged on the same side of the electronic device 20, butthe present disclosure is not limited thereto. FIG. 26 and FIG. 27 areschematic views of an electronic device according to another embodimentof the present disclosure. In some cases, the receiving device 11, theprojection device 12 and the image capturing unit 21 are arranged on oneside of the electronic device 20, while the screen 23 is arranged on theopposite side of the electronic device 20.

14th Embodiment

FIG. 28 is a schematic view of an image recognition device according tothe 14th embodiment of the present disclosure. In this embodiment, animage recognition device 30 includes a host computer 31, a display unit32 and the detecting module 10 disclosed in the 12th embodiment.

The display unit 32 is electrically connected to the host computer 31,and the detecting module 10 is electrically connected to the hostcomputer 31 and the display unit 32. The image recognition device 30captures an image of a user by the detecting module 10, and provides thefunctionality of motion detection and facial recognition by imageprocessing software installed in the host computer 31.

The smartphone (such as the electronic device 20 shown in the 13thembodiment) is only exemplary for showing the detecting module 10installed in an electronic device, and the present disclosure is notlimited thereto. The detecting module 10 can be optionally applied tooptical systems with a movable focus. Furthermore, the lens system andthe imaging lens assembly of the detecting module 10 feature goodaberration corrections and high image quality, and can be applied to 3Dimage capturing applications, in products such as digital cameras,mobile devices, digital tablets, smart televisions, network surveillancedevices, dashboard cameras, vehicle backup cameras, multi-cameradevices, image recognition systems, motion sensing input devices,wearable devices and other electronic imaging devices.

The foregoing description, for the purpose of explanation, has beendescribed with reference to specific embodiments. It is to be noted thatTABLES 1-22 show different data of the different embodiments; however,the data of the different embodiments are obtained from experiments. Theembodiments were chosen and described in order to best explain theprinciples of the disclosure and its practical applications, to therebyenable others skilled in the art to best utilize the disclosure andvarious embodiments with various modifications as are suited to theparticular use contemplated. The embodiments depicted above and theappended drawings are exemplary and are not intended to be exhaustive orto limit the scope of the present disclosure to the precise formsdisclosed. Many modifications and variations are possible in view of theabove teachings.

What is claimed is:
 1. An electronic device comprising: a lens systemcomprising four lens elements which are, in order from an outer side toan inner side, a first lens element, a second lens element, a third lenselement and a fourth lens element; wherein the first lens element has anouter-side surface being convex in a paraxial region thereof, the thirdlens element has an inner-side surface being concave in a paraxialregion thereof, the fourth lens element has an outer-side surface beingconcave in a paraxial region thereof and an inner-side surface beingconvex in a paraxial region thereof, at least one lens element of thelens system has an Abbe number smaller than 22.0, an axial distancebetween the third lens element and the fourth lens element is largerthan each of an axial distance between the first lens element and thesecond lens element and an axial distance between the second lenselement and the third lens element, and a central thickness of the firstlens element is larger than a central thickness of the fourth lenselement; wherein a maximum value among refractive indices of all lenselements of the lens system is Nmax, and the following condition issatisfied:1.50<Nmax<1.70.
 2. The electronic device of claim 1, wherein the firstlens element has positive refractive power, and the second lens elementhas an outer-side surface being convex in a paraxial region thereof. 3.The electronic device of claim 1, wherein an axial distance between theouter-side surface of the first lens element and the inner-side surfaceof the fourth lens element is TD, and the following condition issatisfied:1.0 [mm]<TD<5.0 [mm].
 4. The electronic device of claim 1, wherein amaximum effective radius of the outer-side surface of the first lenselement is Y11, a maximum effective radius of the inner-side surface ofthe fourth lens element is Y42, and the following condition issatisfied:0.30<Y42/Y11<1.0.
 5. The electronic device of claim 1, wherein acurvature radius of an outer-side surface of the third lens element isR5, a maximum effective radius of the outer-side surface of the thirdlens element is Y31, and the following condition is satisfied:0.77≤|R5/Y31|<1.50.
 6. The electronic device of claim 1, wherein amaximum effective radius of the inner-side surface of the fourth lenselement is Y42, an entrance pupil diameter of the lens system is EPD,and the following condition is satisfied:0.10<(Y42×2)/EPD<1.20.
 7. The electronic device of claim 1, wherein eachof at least two lens elements of the lens system has an Abbe numbersmaller than 26.0.
 8. The electronic device of claim 1, wherein at leasthalf of lens elements of the lens system are made of plastic material,and each of the plastic lens elements has two aspheric surfaces; whereina temperature coefficient of refractive index of each of the lenselements is dn/dt, and the following condition is satisfied:−150×10−6[1/° C.]<dn/dt<−50×10−6 [1/° C.]
 9. The electronic device ofclaim 1, further comprising an aperture stop disposed on the outer sideof the first lens element.
 10. The electronic device of claim 1, whereina sum of central thicknesses of all lens elements of the lens systemranges between 0.50 mm and 3.0 mm.
 11. The electronic device of claim 1,wherein at least one surface of the four lens elements has at least oneinflection point.
 12. The electronic device of claim 1, wherein a focallength of the third lens element has a same sign as a focal length ofthe fourth lens element.
 13. An electronic device comprising: a lenssystem comprising four lens elements which are, in order from an outerside to an inner side, a first lens element, a second lens element, athird lens element and a fourth lens element; wherein the first lenselement has an outer-side surface being convex in a paraxial regionthereof, the second lens element has an inner-side surface being concavein a paraxial region thereof, the third lens element has an outer-sidesurface being convex in a paraxial region thereof and an inner-sidesurface being concave in a paraxial region thereof, the fourth lenselement has an outer-side surface being concave in a paraxial regionthereof and an inner-side surface being convex in a paraxial regionthereof, at least one lens element of the lens system has an Abbe numbersmaller than 22.0, an axial distance between the third lens element andthe fourth lens element is larger than each of an axial distance betweenthe first lens element and the second lens element and an axial distancebetween the second lens element and the third lens element, and acentral thickness of the first lens element is larger than a centralthickness of the fourth lens element.
 14. The electronic device of claim13, wherein the first lens element has an inner-side surface beingconcave in a paraxial region thereof.
 15. The electronic device of claim13, wherein the second lens element has an outer-side surface beingconvex in a paraxial region thereof.
 16. The electronic device of claim13, wherein a curvature radius of the outer-side surface of the thirdlens element is R5, a maximum effective radius of the outer-side surfaceof the third lens element is Y31, and the following condition issatisfied:|R5/Y31|<1.50.
 17. The electronic device of claim 13, wherein the firstlens element has positive refractive power; wherein a maximum effectiveradius of the outer-side surface of the first lens element is Y11, amaximum effective radius of the inner-side surface of the fourth lenselement is Y42, and the following condition is satisfied:0.30<Y42/Y11<1.0.
 18. The electronic device of claim 13, wherein anaxial distance between the outer-side surface of the first lens elementand the inner-side surface of the fourth lens element is TD, and thefollowing condition is satisfied:1.0 [mm]<TD<5.0 [mm].
 19. The electronic device of claim 13, whereineach of at least two lens elements of the lens system has an Abbe numbersmaller than 26.0.
 20. The electronic device of claim 13, furthercomprising an aperture stop disposed on the outer side of the first lenselement.
 21. The electronic device of claim 13, wherein at least onesurface of the four lens elements has at least one critical point. 22.The electronic device of claim 13, wherein at least one fittingstructure is disposed between adjacent lens elements of the lens system.23. The electronic device of claim 13, wherein the central thickness ofthe first lens element is larger than a central thickness of the secondlens element.
 24. The electronic device of claim 13, wherein a centralthickness of the second lens element is larger than a central thicknessof the third lens element.